A sample of radioactive substance is found 90% of its initial amount after one day . What % of the original sample can be found after 3 days?

Options

A. 81
B. 72.9
C. 25
D. 65.61

Answer

To solve the problem of how much of the original radioactive substance remains after 3 days, we can follow these steps:

### Step 1: Understand the initial condition
Initially, we have 100% of the radioactive substance. After 1 day, we are told that 90% of the initial amount remains. This means that 10% has decayed.

### Step 2: Determine the remaining fraction after 1 day
After 1 day, the remaining fraction of the substance is:
\[ \text{Remaining fraction after 1 day} = \frac{90}{100} = 0.9 \]

### Step 3: Apply the decay over multiple days
Since the decay is consistent over time, we can express the remaining amount after multiple days using the formula:
\[ \text{Remaining fraction after } n \text{ days} = (\text{Remaining fraction after 1 day})^n \]
In this case, \( n = 3 \) days.

### Step 4: Calculate the remaining fraction after 3 days
Using the formula:
\[ \text{Remaining fraction after 3 days} = (0.9)^3 \]
Now, we calculate \( (0.9)^3 \):
\[ (0.9)^3 = 0.9 \times 0.9 \times 0.9 = 0.729 \]

### Step 5: Convert the remaining fraction to percentage
To express this as a percentage of the original sample:
\[ \text{Remaining percentage after 3 days} = 0.729 \times 100 = 72.9\% \]

### Conclusion
Thus, after 3 days, 72.9% of the original sample of the radioactive substance remains.

---